[Binghamton Geometry/Topology Seminar] November 4

[Lucas Sabalka]

                  BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR

Date:  Thursday, November 4, 2010
Time:  2:50-3:50pm
Place:  Library North 2205 followed by coffee/tea in the Anderson
         Reading Room.

Speaker:  Dima Savchuk (Binghamton)
Title:  Geometry of curve complex analogues for Out(F_n), I

Abstract:  This is the first of two talks based on our joint work with Lucas
Sabalka.  One of the most popular open questions about Out(F_n) - a group of
outer automorphisms of a free group of rank n - is the construction of a
Gromov hyperbolic space on which Out(F_n) naturally acts, extending the deep
analogy between Out(F_n), mapping class groups, and linear groups. Each
mapping class group naturally acts on a curve complex of the surface, which
is hyperbolic due to a celebrated theorem by Masur and Minsky. Many spaces
which could serve as an analogue for this space were proposed in recent
years.  We will define some of them and concentrate mostly on a space named
the ``Free factorization graph''. The main outcome of our work is that this
space in not hyperbolic, so it should not be considered as an analogue to
curve complex.

The first talk will be devoted to the background and introduction to the
ideas and some techniques used in our proof.
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